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This paper estimates the break point for large-dimensional factor models witha single structural break in factor loadings at a common unknown date. First,we propose a quasi-maximum likelihood (QML) estimator of the change point basedon the second moments of factors, which are estimated by principal componentanalysis. We show that the QML estimator performs consistently when thecovariance matrix of the pre- or post-break factor loading, or both, issingular. When the loading matrix undergoes a rotational type of change whilethe number of factors remains constant over time, the QML estimator incurs astochastically bounded estimation error. In this case, we establish anasymptotic distribution of the QML estimator. The simulation results validatethe feasibility of this estimator when used in finite samples. In addition, wedemonstrate empirical applications of the proposed method by applying it toestimate the break points in a U.S. macroeconomic dataset and a stock returndataset.

Quasi-maximum likelihood estimation of break point in high-dimensional factor models